Laws of Exponents

Q. If $2^a=3^b=6^c$ then

1. $c=\frac{ab}{a+b}$
2. $c=\frac{a+b}{a-b}$
3. $c=\frac{a{b}^2}{a^2+b^2}$
4. $c=\frac{a{b}^2}{a^2-b^2}$

Q.

If ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$ then find the value of m.

1. $-\frac{1}{3}$

2. $-\frac{1}{7}$

3. $\frac{3}{2}$

4. $\frac{2}{8}$

Q.

What is the value of the expression $\frac{a^m}{a^n}$ ?

1. a^mn

2. a^m-n

3. a^m/n

4. a^m+n

Q.

Simplify ${\left(256\right)}^{\frac{-1}{2}}$.

1. 16

2. $\frac{1}{4}$

3. 4

4. $\frac{1}{16}$

Q. When expanded, the number of zeroes in ${1000}^{10}$ is ______.

1. 30
2. 4
3. 13
4. 10

Q. The value of $\frac{(0.6{)}^0-(0.1{)}^{-1}}{\left(\frac{3}{2^3}{)}^{-1}\right(\frac{3}{2}{)}^3+(-\frac{1}{3}{)}^{-1}}$ is _____________.

1. $\frac{3}{2}$
2. $\frac{-3}{2}$
3. $\frac{2}{3}$
4. $\frac{-1}{2}$

Q. Simplify:${64}^{\frac{1}{3}}[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]$

1. $\frac{1}{3}$
2. $-3$
3. $\frac{2}{3}$
4. $(3{)}^{-2}$

Q.

$\text{If}{\left(\sqrt{1024}\right)}^3=8^x\text{, then}x\text{is}$ ________.

1. 5

2. 10

3. 2

4. 15

Q.

Simplify $\frac{{27}^{\frac{2}{3}}}{9^{\frac{1}{2}}{3}^{\frac{3}{2}}}$

1. 1÷√3

2. √3

3. 3√3

4. 1÷3√3

Q. Solve for $x$ in the equation $2^{x+1}=8^x.$

1. $\frac{-1}{3}$
2. $\frac{1}{2}$
3. 1
4. 3